My folks lived in town for a time. Dad and I built unobstrusive box traps from Ragnor Benson designs. A peice of plywood was leaned against the garage and the trap was placed under it. Sort of like making a tunnel for the critter to walk into. Dad caught many animals. He simply took the trap into the garage. Then he reached in with heavy welding gloves and off'd the critter with a ball peen hammer. Feral cats were the common pests he caught. Silent and deadly.
Skunks were drowned inside the traps as they get fussy and will spray. Dad just lowered the trap into a section of metal ducting and filled it with water.
If the area critters get wise and stay away from the trap, try this old trick. Place an opened can of cheap catfood inside the box trap but don't set the trigger. After awhile, they get used to the free meal. Then you simply set the trigger and start catching again.
Plan to dispose of the corpses with care. Dad dumped 'em alongside the road a mile or so away. Hey, crows gotta eat, too! Its a good idea to be somewhat cautious and elusive.
Fire up the grill! Deer hunting IS NOT catch and release.